PDEs you should know

I know I could look it up but having an explanation of what any of the variables mean would make this not useless.

Partial Differential Equations you should know but with no explanation...I mean...shouldn't you...just know? /s

PDEs are really useful if you are in the rare domains where they are useful. But most PDEs don't have even have closed form solutions for non-trivial boundary conditions. So unless you are a physicist or something adjacent, no, no you really don't need to know these.

Hard to say what's the intended audience for the page though. Could be a message aimed at physics undergrads or something. If so, then indeed, you should know these.

what's the best black scholes tutorial?